HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 245
Example, Example 1, Example 2
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hp40g+.book Page 63 Friday, December 9, 2005 1:03 AM CYCLOTOMIC EXP2HYP Example Find the solutions P(X) of: P(X) = X (mod X2 + 1) P(X) = X - 1 (mod X2 - 1) Typing: CHINREM((X) AND (X2 + 1), (X - 1) AND (X2 - 1)) gives: -x---2----------2---x----+-----1-- AND x---4----------1- 2 2 That is: P[X] = --x--2----------2---x----+-----1-2 ⎝⎛ mod - x---4---2-------1-⎠⎞ Returns the cyclotomic polynomial of order n. This is a polynomial having the nth primitive roots of unity as zeros. CYCLOTOMIC has an integer n as its argument. Example 1 When n = 4 the fourth roots of unity are {1, i, -1, -i}. Among them, the primitive roots are: {i, -i}. Therefore, the cyclotomic polynomial of order 4 is (X - i).(X + i) = X2 + 1. Example 2 Typing: CYCLOTOMIC(20) gives: x8 - x6 + x4 - x2 + 1 EXP2HYP has an expression enclosing exponentials as an argument. It transforms that expression with the relation: exp(a) = sinh(a) + cosh(a). Computer Algebra System (CAS) 14-63